Multilevel Coding Scheme for Integer-Forcing MIMO Receivers With Binary Codes

An integer-forcing (IF) linear multiple-input multiple-output (MIMO) receiver has recently been proposed, which is theoretically shown to achieve near capacity with almost the same complexity as that of conventional linear receivers. The key idea is that the receiver attempts to directly decode integer-linear combinations of codewords. To ensure that this sum-decoding operation is feasible, in previous works, lattice codes over $\mathbb {Z}_{q}$ were employed. Although those codes can attain good theoretical performance, however, its implementation complexity can be considerably high in practice, especially when $q$ is large to support high-order modulations. In this paper, we propose a practical multilevel coding scheme for IF MIMO, in which multilevel encoding composed of binary linear codes $(q = 2)$ in conjunction with the natural mapping is employed on the transmitter side and multistage decoding adapted to the IF operation is employed on the receiver side. The performance of the proposed scheme is extensively evaluated both analytically and numerically, showing that the gain of IF over conventional receivers is indeed achievable in practical settings with almost the same complexity. Our results imply that the proposed IF MIMO can be an attractive solution for the 5G communications due to its ability of supporting high spectral efficiency with low complexity.

I. Introduction

Multiple-input multiple-output (MIMO) antenna technique can significantly improve the capacity of a wireless system with respect to the number of antennas [1], [2]. If channel state information at the transmitter (CSIT) is available, the capacity can be simply achieved by the linear singular value decomposition (SVD) beamforming and water-filling power allocation [3], with no need to consider complex algorithms such as the joint maximum likelihood (ML) decoding. In practice, however, the acquisition of CSIT is often quite challenging due to limited feedback or channel variation. In the lack of CSIT, the performance of conventional linear receivers such as the minimum mean-squared error (MMSE) receiver becomes far apart from the capacity, especially when the channel matrix is near-singular [4]–[7]. Non-linear MIMO schemes such as sphere decoding can provide an enhanced performance and its complexity reduction algorithms have also been proposed in [8]–[11]. Their complexities, however, are yet considerably high to be applicable to practical systems, especially when the number of antennas is large and/or the modulation order is high. Note that in the current Long Term Evolution-Advanced (LTE-Advanced) system, the fourth generation (4G) communications system, up to eight streams with 256-quadrature amplitude modulation (QAM) are supported for high data rate transmission, and it is highly likely that the number of supported streams and/or the supported modulation order will further increase in the next fifth generation (5G) communications system. Hence, it becomes more and more important to design a practical MIMO receiver that can support high spectral efficiency with low complexity.